# Definition:Linear Operator/Vector Space

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## Definition

A **linear operator** on a vector space is a linear transformation from a vector space into itself.

## Also known as

A **linear operator** in this context is also known as a **linear function**.

## Sources

- 1955: John L. Kelley:
*General Topology*... (previous) ... (next): Chapter $0$: Algebraic Concepts - 1974: Robert Gilmore:
*Lie Groups, Lie Algebras and Some of their Applications*... (previous) ... (next): Chapter $1$: Introductory Concepts: $1$. Basic Building Blocks: $4$. LINEAR VECTOR SPACE: Example $3$